Expeient #10 Bio-Physics Pe-lab Questions ** Disclaie: This pe-lab is not to be copied, in whole o in pat, unless a pope efeence is ade as to the souce. (It is stongly ecoended that you use this docuent only to geneate ideas, o as a efeence to explain coplex physics necessay fo copletion of you wok.) Copying of the contents of this web site and tuning in the ateial as oiginal ateial is plagiais and will esult in seious consequences as deteined by you instucto. These consequences ay include a failing gade fo the paticula pe-lab o a failing gade fo the entie seeste, at the discetion of you instucto. ** 1) Let s say you had to ove the with a leve. You could use the Moon as a pivot point. Calculate how long of a leve you would need. It will be gigantic! This is the classic see-saw poble. Hee is ou geneal setup of the see-saw: We have the on one side of the see-saw, the Moon is ou pivot point, and soe ando nedy guy on the othe side of the see-saw (since this is a physics poble, we need the nedy guy). ** Note that we ae assuing the weight of the bea to be negligible. ** Woohoo! igue 1: Setup of the Poble Move the with a Leve ** Note that the, Moon, Sun and Head of the Goofy Physics Guy ae not to scale. That is, the oon ay actually be salle then shown. ** o the sake of aguent, let s say that this expeient is being pefoed on the sun. (I ean coe on we e aleady oving the why not?!?! We have to do this since we need soe efeence fae with a ass to povide acceleation due to gavity. Typically we have the whee the acceleation due to gavity is g = 9.81 /s ; howeve, since we e oving the, it doesn t ake uch sense to have the ON the. That would equie two s that s eally deep philosophy. )
We ll call the acceleation due to gavity on the sun, g sun. If we daw in the vaious foces and distances, we get the following setup: igue : Expeiental Setup on Sola Refeence ae Soe paaetes which ay be useful fo solving this poble wee given: oce due to Mass of the and Acceleation due to Gavity on the Sun (N) Distance to the Moon (k) oce due to Mass of Soe Goofy Physics Guy and Acceleation due to Gavity on the Sun (N) 5.86 x 10 5 384000 1000 What we ae fist tying to find is what is the iniu length that ust be fo the Moon in ode to stat to ove the. That is, we want the toque ceated by to be geate then the toque ceated by the. We know the definition of agnitude of the toque is given by: sin We e going to assue that the angles between the foces and the leve s ae all nealy 90 degees, because that akes the ath A LOT EASIER. (They ay in actuality be like 89.99999999999999 degees, but that s close enough to 90 degees.) sin 90 o
Thus: and Exaining the oiginal inequality: Thus, the iniu distance ust be away fo the oon is: Plugging in the values we wee given poduces the following: 4 384000 k5.8610 N 1000 N 8.50410 k So, in ode to lift the eath with just his own body weight, ust have a leve of at least.504 x 10 8 kiloetes! (Notice this is only s leve, not the entie length of the leve.) To get a pettie nube, let s convet this value to light-yeas. (Notice that light-yeas is a weid nae fo a distance, but IT IS a distance. It is the distance light takes to tavel one yea. That is, if I ceated a bea of light ight this second, in one yea [007] it would be a distance of 1 light-yea away fo y cuent location.) The convesion facto fo kiloetes to light-yeas is: 1 ly 9.4610 1 k 8 1 ly.504 10 k.37868910 1 9.46 10 k 15 ly 15.37868910 ly So the iniu length of s leve ust be at least,78,689,000,000,000 lightyeas long. Needless to say, that s a long distance. So if we ceated a bea of light ight this second, it would get thee in Novebe of the yea 7868900000006.
Now, to answe the actual question: How long of a leve you would need? The total length of the leve will be the length of the s adial and s adial sued togethe. Leve Length 384000 k.50410 k 8 Leve Length 8 Leve Length.5040000000000000000038400010 k 15 Leve Length.37868910 ly So, you can see that the ajoity of the length of the entie leve is due to the side that is sitting on. In conclusion: o all you cazy people that want to single-handedly ove the with a giant leve that has the Moon as its pivot point just fah-getta-bout-it. ) Use the following paaetes and the expeiental setup to calculate values fo given that: (c) (c) (c) (g) (g) 10 5 60 45 0 igue 3: Expeiental Setup of a Bicep Suppoting a Massive Load In the setup above, thee ae thee toques (ecall that a toque is foce acting at a adial ): 1. [ ] = The ass hanging (foce) at the end of the length (adial ).
. [ ] = The holding (foce) the length staight (adial ). 3. [ ] = The ass of the length itself hanging (foce) at the cente of ass (adial ). o static equilibiu (whee nothing is otating/oving) the net su of the toques acting on the syste ust add up to zeo. (Reebe we use the geek lette tao fo toque.) n i1 i 0 So, fo ou syste, we have thee toques; so, fo static equilibiu, we ust have: 3 i1 i 1 3 0 o this expeient, we will always foce (no pun intended) the to be level (again no pun intended). That is, we want the to be pefectly paallel hoizontally with the table. This will geatly siplify the calculation fo the toques due to the and the. If we explicitly wite out each of the thee toques: Toque 1 (due to ): ist, ecall the definition of toque: To find the diection of the toque, we need to use the ight-hand ule. ist point you finges in the diection of then cul the to the diection of. The diection you thub points is the diection of the toque fo the coss poduct. o this case, is pointing to the ight (so point you pointe-to-pinky finges in the ight diection), and is pointing down (keeping you finges in the ight diection, twist you hand (pal down) so when you bend you finges they ae pointing down. You thub should be pointing away fo you. This eans that the diection of the otation is clockwise (nod you hand up and down while keeping you thub pointing away fo you and you ll see that the diection fo you knuckles to you finge tips is in the clockwise diection) and the sign of the toque is negative). ** Aside ** I can neve eebe the ighty-tighty, lefty-loosy thing y dad taught e fo scews, especially when I on by back. When I want to know which way I want the scew to go, I siply use the diection of toque (because that s exactly what I doing). If I want the scew to go away fo e, I point y thub in that diection and see that the otation diection fo y knuckles to y finge tips is in the clockwise diection. If I want the
scew to go towad e, I point y thub in that diection and see that the otation diection fo y knuckles to y finge tips is in the counte-clockwise diection. ** End Aside ** By the ight-hand ule: sin And since the angle (by design) between the foce and the leve is 90 degees: Toque (due to ): To find the diection of this toque, is pointing to the ight (so point you pointe-topinky finges in the ight diection), and is pointing leftish-up (keeping you finges in the ight diection, twist you hand (pal up) so when you bend you finges they ae pointing backwads. You thub should be pointing towad you. This eans that the diection of the otation is counte-clockwise (nod you hand up and down while keeping you thub pointing towad you and you ll see that the diection fo you knuckles to you finge tips is in the counte-clockwise diection) and the sign of the toque is positive). By the ight-hand ule: Toque 3 (due to ): sin To find the diection of this toque, is pointing to the ight (so point you pointe-topinky finges in the ight diection), and is pointing down (keeping you finges in the ight diection, twist you hand (pal down) so when you bend you finges they ae pointing down. You thub should be pointing away fo you. This eans that the diection of the otation is clockwise and the sign of the toque is negative). By the ight-hand ule: sin And since the angle (by design) between the foce and the leve is 90 degees: Binging it all togethe:
Now, if we add each of these up and set thei su equal to zeo, we have the static equilibiu equation: 3 i1 i 0 sin 0 sin Solve this fo the foce acting on the. 0 g sin sin g g sin g We ae given the distances and the asses, and we know the acceleation due to gavity; so, fo any give theta we can calculate the foce on the. (c) (c) (c) (g) (g) 10 5 60 45 0 ist though, we need to convet all the distances to etes and all the asses to kilogas: () () () (kg) (kg) 0.10 0.5 0.60 0.045 0.00 o Calculate fo θ = 90 g sin g 9.81 s s.60.0kg 9.81 0.50.045kg 0 o 0.1sin 90 o Calculate fo θ = 45. 8085 N
9.81 s s.60.0kg 9.81 0.50.045kg 0 o 0.1sin 45 o Calculate fo θ = 160 3. 557 N 9.81 s s.60.0kg 9.81 0.50.045kg 0 o 0.1sin 160 6. 66869 N